Related papers: Pattern avoidance by even permutations
The concept of pattern avoidance respectively containment in permutations can be extended to permutations on multisets in a straightforward way. In this note we present a direct proof of the already known fact that the well-known…
This paper considers the enumeration of trees avoiding a contiguous pattern. We provide an algorithm for computing the generating function that counts n-leaf binary trees avoiding a given binary tree pattern t. Equipped with this counting…
We consider a large family of equivalence relations on permutations in Sn that generalise those discovered by Knuth in his study of the Robinson-Schensted correspondence. In our most general setting, two permutations are equivalent if one…
Vincular and covincular patterns are generalizations of classical patterns allowing restrictions on the indices and values of the occurrences in a permutation. In this paper we study the integer sequences arising as the enumerations of…
The aim of this paper is two-fold. We first prove several new interpretations of a kind of $(q,t)$-Catalan numbers along with their corresponding $\gamma$-expansions using pattern avoiding permutations. Secondly, we give a complete…
We introduce "fertility Wilf equivalence," "strong fertility Wilf equivalence," and "postorder Wilf equivalence," three variants of Wilf equivalence for permutation classes that formalize some phenomena that have appeared in the study of…
We present two families of Wilf-equivalences for consecutive and quasi-consecutive vincular patterns. These give new proofs of the classification of consecutive patterns of length $4$ and $5$. We then prove additional equivalences to…
Let $T_n$ be the set of 321-avoiding permutations of order $n$. Two properties of $T_n$ are proved: (1) The {\em last descent} and {\em last index minus one} statistics are equidistributed over $T_n$, and also over subsets of permutations…
In this paper, we prove two conjectures of Egge on the enumeration of several classes of pattern-avoiding Fishburn permutations. Our results include enumerating Fishburn permutations avoiding pattern 321 and one of the following three types…
We discuss a new notion of pattern avoidance motivated by the operad theory: pattern avoidance in planar labelled trees. It is a generalisation of various types of consecutive pattern avoidance studied before: consecutive patterns in words,…
The Stanley-Wilf limit of the pattern 1324 is known to lie between 10.271 and 13.5. We obtain lower bounds on this limit by encoding permutations as walks in directed graphs: building a permutation by successive insertion of maxima…
We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain…
Building off recent work of Garg and Peng, we continue the investigation into classical and consecutive pattern avoidance in rooted forests. We prove a forest analogue of the Stanley-Wilf conjecture for avoiding a single pattern as well as…
The existence of apparently coincidental equalities (also called Wilf-equivalences) between the enumeration sequences, or generating functions, of various hereditary classes of combinatorial structures has attracted significant interest. We…
Let T_k^m={\sigma \in S_k | \sigma_1=m}. We prove that the number of permutations which avoid all patterns in T_k^m equals (k-2)!(k-1)^{n+1-k} for k <= n. We then prove that for any \tau in T_k^1 (or any \tau in T_k^k), the number of…
For a set of permutation patterns $\Pi$, let $F^\text{st}_n(\Pi,q)$ be the st-polynomial of permutations avoiding all patterns in $\Pi$. Suppose $312\in\Pi$. For a class of permutation statistics which includes inversion and descent…
We classify all bi-vincular patterns of length two and three according to the number of permutations avoiding them. These patterns were recently defined by Bousquet-Melou et. al., and are natural generalizations of Babson and…
Evil-avoiding permutations, introduced by Kim and Williams in 2022, arise in the study of the inhomogeneous totally asymmetric simple exclusion process. Rectangular permutations, introduced by Chiriv\`i, Fang, and Fourier in 2021, arise in…
Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…
Egge conjectured that permutations avoiding the set of patterns $\{2143,3142,\tau\}$, where $\tau\in\{246135,254613,263514,524361,546132\}$, are enumerated by the large Schr\"oder numbers. Consequently, $\{2143,3142,\tau\}$ with $\tau$ as…